We present a rigorous method for estimating some of the calibration parameters in airborne laser scanning (ALS), namely the three bore-sight angles and the range-finder offset. The technique is based on expressing the system calibration parameters within the directgeoreferencing equation separately for each target point, and conditioning a group of points to lie on a common surface of a known form such as a plane. However, the assumed a priori information about q chosen planar features is only their form not the spatial orientation or position. Thus, the 4·q plane parameters are estimated together with the calibration parameters in a combined adjustment model that makes use of GPS/INS-derived position and orientation as well as LiDAR range and encoder angle as observations. To make the approach practical when working with voluminous ALS and GPS/INS data, the contribution of each laser point to the normal equations is formed sequentially. The discussions focus on practical examples with data from a continuouslyrotating scanner that reveal the conditions under which almost complete de-correlation between the estimated parameters occurs. In such a case, all bore-sight angles are determined with accuracy that is several times superior to the system noise level. Given sufficiently strong geometry, the presented method is shown to be not only accurate but also very robust in terms of convergence. When appropriate, the method is applicable for calibration of additional systematic effects such as laser-beam encoder offsets or scale factor with minimal modification to the functional model.

This article presents a new estimation method for the parameters of a time series model. We consider here composite Gaussian processes that are the sum of independent Gaussian processes which, in turn, explain an important aspect of the time series, as is the case in engineering and natural sciences. The proposed estimation method offers an alternative to classical estimation based on the likelihood, that is straightforward to implement and often the only feasible estimation method with complex models. The estimator furnishes results as the optimization of a criterion based on a standardized distance between the sample wavelet variances (WV) estimates and the model-based WV. Indeed, the WV provides a decomposition of the variance process through different scales, so that they contain the information about different features of the stochastic model. We derive the asymptotic properties of the proposed estimator for inference and perform a simulation study to compare our estimator to the MLE and the LSE with different models. We also set sufficient conditions on composite models for our estimator to be consistent, that are easy to verify. We use the new estimator to estimate the stochastic error's parameters of the sum of three first order Gauss-Markov processes by means of a sample of over 800,000 issued from gyroscopes that compose inertial navigation systems. Supplementary materials for this article are available online.

-In this article, we investigate two different algorithms for the integration of GPS with redundant MEMS-IMUs. Firstly, the inertial measurements are combined in the observation space to generate a synthetic set of data which is then integrated with GPS by the standard algorithms. In the second approach, the method of strapdown navigation needs to be adapted in order to account for the redundant measurements. Both methods are evaluated in experiments where redundant MEMSIMUs are fixed in different geometries: orthogonallyredundant and skew-redundant IMUs. For the latter configuration, the performance improvement using a synthetic IMU is shown to be 30% on the average. The extended mechanization approach provides slightly better results (about 45% improvement) as the systematic errors of the individual sensors are considered separately rather than their fusion when forming compound measurements. The maximum errors are shown to be reduced even by a factor of 2.

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